Aspects of WZW models at critical level

✍ Scribed by I. Bakas; C. Sourdis

• Publisher: John Wiley and Sons
• Year: 2005
• Tongue: English
• Weight: 115 KB
• Volume: 53
• Category: Article
• ISSN: 0015-8208
• DOI: 10.1002/prop.200510198

✦ Synopsis

Abstract

We consider non‐compact WZW models at critical level (equal to the dual Coxeter number) as tensionless limits of gravitational backgrounds in string theory. Special emphasis is placed on the Euclidean black hole coset SL(2,R)~k~/U(1) when k = 2. In this limit gravity decouples in the form of a Liouville field with infinite background charge and the world‐sheet symmetry of the model becomes a truncated version of W~∞~ without Virasoro generator. This is regarded as manifestation of Langlands duality for the SL(2,R)~k~ current algebra that relates small with large values of the level in the two extreme limits. However, the physical interpretation of the SL(2,R)~k~/U(1) coset model below the self‐dual value k = 3 remains elusive including the non‐conformal theory at k = 2.